Accurate Estimations of Any Eigenpairs of N -th Order Linear Boundary Value Problems

Pedro Almenar and Lucas Jódar
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Pedro Almenar: Vodafone Spain, Avda. América 115, 28042 Madrid, Spain
Lucas Jódar: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Mathematics, 2021, vol. 9, issue 21, 1-22

Abstract: This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n -th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on the selection of a particular type of cone for each eigenpair to be determined, the recursive application of the operator associated to the equivalent integral problem to functions belonging to such a cone, and the calculation of the Collatz–Wielandt numbers of the resulting functions.

Keywords: n -th order linear differential equation; two-point boundary value problem; sign-regular kernel; eigenvalue; eigenfunction; Collatz–Wielandt numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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